Placing the device-under-test (DUT) in a grounded metal box with a broadband antenna inside.
Well, that's great for screening out any external emissions -- that's why why the EMI/RFI test labs all have RF Screen Rooms. See for example this vendor but there are many, many others. BUT, screen rooms are typically not used with antenna measurements. The problem is reflections. The reflected signal will generate hot spots and cold spots (constructive and destructive interference) which will make the measurement very unreliable.
Also, you'd have to make sure you have enough room that your device under test is located far enough from your antenna to be in its far field.
This is why the test houses will typically have an RF anechoic chamber and will do all their antenna-based testing in there. Hopefully the anechoic chamber also has screening against outside RF. But typically what I've seen is the test houses just perform their testing in a large open space. (Without any RF shielding, unfortunately. On one occasion I had to... invest... a bunch of time to prove that the spurious signal they were seeing was not from the device under test...)
for first-pass testing on prototypes
For super-basic first pass testing I've always seen people just use sniffer probes. When I typed the phrase "sniffer probe" into Google I was shocked to see probes selling for $500. Every sniffer probe I've ever seen has been home-brew for a few bucks:
- For low frequencies (up to a few MHZ) just clip the ground lead of an oscilloscope probe to its input and treat it like a loop antenna. Works decently well for finding loud RF signals.
- For much higher frequencies (up to a GHz or so), cut a coax cable and solder a small copper loop (maybe the diameter of a pencil) to the signal and ground leads.
Typically people use these sniffer probes to poke around the circuit and look for any nasty surprises. This little "antenna" is decidedly not calibrated, but typically first-pass testing is just "look for any loud unexpected signals" and a sniffer probe gets that job done. Once things look good with that quick-and-dirty test, then it's probably time to pay those big bucks to the test lab to get that trusted measurement.